Um estudo de área e perímetro por meio da resolução de problemas com estudantes do 6ª ao 8º ano do ensino fundamental

Abstract

This study aims to investigate the process of knowledge construction regarding the area and perimeter of plane figures by students from the 6th to the 8th grade of elementary school through a teaching sequence based on problem-solving within the Experimental Practices Integrative Component of a state public school in the city of Ituiutaba/MG. The ideas of Allevato and Onuchic (2014) underpinned the research, which has a qualitative character based on the Teaching-Learning-Assessment methodology of Mathematics through Problem Solving, and involved the participation of 50 students, 24 from the 6th grade, 12 from the 7th grade, and 14 from the 8th grade. Data were collected through a teaching intervention that took place over 5 meetings, each lasting 1 hour and 40 minutes. In each meeting, participants received a sheet containing 2 problems each involving the content of area and perimeter of plane figures. The analysis was structured across 5 meetings, following the 10-step roadmap proposed by Allevato and Onuchic (2014). The research results highlight that the students demonstrated progress in understanding the concepts covered, especially in recognizing properties of plane figures, such as the equality of opposite sides in a rectangle and the equivalence of areas in different geometric configurations. A greater ease in calculating areas from known references, such as the square and the rectangle, was also observed, as well as the frequent use of visual representations and annotations on drawings to support the organization of thought. However, most did not use abstract formulas to perform the calculations. Many students showed a tendency to operate directly with the presented numbers, without explaining the geometric meaning of their actions, revealing a more procedural than conceptual approach. Keywords: